Finite Basis Of Identities Research Articles

IDENTITIES OF ALMOST STABLE GROUP REPRESENTATIONS

It is proved that almost stable group representations over a field have a finite basis of identities. Moreover, a variety generated by an arbitrary almost stable representation is Specht and all of its subvarieties have a finite uniformly bounded basis rank. In particular, the identities of an arbitrary representation of a finite group are finitely based.Bibliography: 17 titles.

Minimal non-permutative pseudovarieties of semigroups III

Various types of permutativity conditions are important in the study of (pseudo)varieties of semigroups. In previous papers of this series, minimal pseudovarieties failing certain permutativity conditions were determined. This theme is pursued here in relation to a family of conditions which appear in the investigation of power pseudovarieties of semigroups, namely, for eachk≥0, we consider the conditionC k on a semigroup that it satisfy the identityx 1 ...x k y 1 y 2 z 1 ...z n=x 1 ...x k y 2 y 1 z 1 ...z n for somen. For all minimal pseudovarieties failing Ck, a generator and finite basis of identities are specified.

Example of a variety of solvable alternative algebras over a field of characteristic 2 having no finite basis of identities

Example of a variety of solvable alternative algebras over a field of characteristic 2 having no finite basis of identities

Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties

We introduce new sufficient conditions for a finite algebraU to possess a finite basis of identities. The conditions are that the variety generated byU possess essentially only finitely many subdirectly irreducible algebras, and have definable principal congruences. Both conditions are satisfied if this variety is directly representable by a finite set of finite algebras. One task of the paper is to show that virtually no lattice varieties possess definable principal congruences. However, the main purpose of the paper is to apply the new criterion in proving that every para primal variety (congruence permutable variety generated by finitely many para primal algebras) is finitely axiomatizable. The paper also contains a completely new approach to the structure theory of para primal varieties which complements and extends somewhat the recent work of Clark and Krauss.